Triangle calculator



Dec. 19, 1950 Filed June 17, 1949 W. H. JENSEN TRIANGLE CALCULATOR 3Sheets-Sheet 1 I N VE N TOR.

W/LL FROMIENSE/V,

BY 2444M Dec. 19, 1950 w, H, JENSEN I 2,534,601

TRIANGLE CALCULATOR Filed June 17,1949 3 Sheets-Sheet 2 Patented Dec.19, 1950 UNITED STATES. PATENT OFFICE TRIANGLE CALCULATOR Willard H.Jensen, Longview, Tex.

Application June 17,1949, Serial No. 99,790

s 4 Claims.

This invention relates to calculators for aiding in the solution oftrigonometric problems.

The primary object of the invention is to provide a simple mechanicalcalculator for solving triangles.

A more specific object of the invention is to provide a mechanicalcalculator which is capable of assisting in the solving for unknownvalues of both right and oblique triangles.

With the foregoing and other objects in mind, the invention resides inthe following specification and appended claims, certain embodiments anddetails of construction of which are shown in the drawings in which:

Figure 1 is a plan view of the calculator,

Figure 2 is a plan view of the opposite side of the calculator fromFigure 1,

Figure 3 is a View in side elevation of Figure 1,

Figure 4 is a view in side elevation of Figure 2, and

Figures 5, 6, 7, 8 and. 9 are segmental Views'of rotatable disk membersused in the calculator.

Referring more particularly to Figures 1 and 3 a pair of circular platesI and 2 are shown suitably spaced apart by spacers 3. The plates arepreferably made of opaque plastic, although other material such as woodor metal would be satisfactory for the purpose. Inscribed on the surfaceof plate I is a right triangle 4 having sides 5, 6 and I andcomplementary angles D and E. Within the complementary angles of thetriangle are windows 8 and 9 in plate I. Associated with sides 5, 6 and-I are windows I 0, II and I2 respectively provided in plate I. Inscribedin the surface of the plate among the windows 5, 6 and l are indicia ofmultiplication, division and directions for instructing the user of thecalculator as will be set forth later in the specification.

Adjacent to the under side of plate I are toothed disks I3, I4, I and I6rotatably mounted on pivots II, I8, I3 and 20 respectively. The teeth ondisk I5, which is the operating disk, mesh with teeth on disks I 6 andI4. The teeth on disk I4 also mesh with the teeth on disk I3. A portionof the periphery of disk'l5 extends beyond the periphery of plate I at2| to facilitate manual movement of disk I5. This disk is provided with50 teeth and has indicia representing angles from 1 to. 45 degrees asshown in Figure 5. Disk I4,

shown partially in Figure '7, is also provided with 50 teeth and hasindicia representing the co-sine and co-tangent functions of thoseangles on disk 15. Disk I3, shown partially in Figure 9, is providedwith 50 teeth and with indicia representing the trigonometric functionsof tangent and the side 6 be one inch for example.

sine of angles on disk I5. The disk I6 is partially shown in Figure 8and is inscribed with indicia representing the trigonometric functionsof sine and co-sine of angles appearing on disk I5.

The operation of the calculator now becomes readily apparent. Forexample, under a given condition of one known complementary angle andone side the other two sides may be readily determined by following thedirection indicia on plate I. Thus move disk I5 until the angle of 15degrees (as shown) appears in window 9. Disks I3, I4 and it areautomatically moved to present trigonometric function values of theangle 15 degrees in windows II], II and I2. Let Then to solve for side5, it is merely necessar to follow the directing indicia arrow from side6 to side 5 and multiply side 6 by the function appearing in window IIIwhich is .2679 or the tangent of 15 degrees. Thus since side 6 is oneinch, the value of side 5 is .2679-inch.

Other calculations are as easily determined. Assume the angle 15 degreesis given along with side I; the problem being to find side 5. Follow thedirecting arrow indicia from side I to side 5 and multiply by thefunction appearing in win dow II] or .2588 which is the sine of 15degrees. Thus if the length of side I is one foot the length of side 5is .2588 foot.

To find side I with the same given angle of 15 degrees and side 5 knownat 10 feet, follow the directing arrow indicia from side 5 to side I anddo what the indicia says-namely, divide side 5 by the function .2588appearing in window I2 which is the sine of 15. degrees. In other words,divide 10 feet by .2588 to arrive at the length of side I.

If the angle E is given it is merely necessary to move disk I5 untilthis angle appears in window 8 at'which point the complementary angle Dappears in window 9 and the procedure is the same as in the aboveexamples.

Referring now to Figures 2, 4 and 6 the plate 2 is shown havinginscribed thereon an oblique triangle 22 having sides 23, 24 and 25.Within each angle of the triangle are windows 26, 2! and 28 in plate 2.Also within the triangle and associated with'the angle windows arewindows 29, 20 and 3| in plate 2. Indicia similar to that used on plateI are used to direct calculations.

Adjacent the under side of plate 2 are identical rotatable disks 32, 33and 34 suitably mounted on pivots 35, 36 and 31. The peripheries ofthese disks extend beyond the peripher of plate 2 to ease themanipulation of same. The disks are each provided with indicia of anglesand sine functions as shown partially in Figure 6.

The plate 2 of the calculator can assist in solving any obliquetriangles having 2 angles and 1 side given, or by merely following thesuitable trigonometric formulae which may be inscribed on the plate 2for solving oblique triangles where two sides and the included angle aregiven.

Calculations are made as follows:

To find side 24 with the angles D and E and side 2e given, follow thedirecting arrow from side 2s to window 3! and multiply (as directed bythe indicia) side 25 by the function in window 5|. Continue to followthe directing arrow from window 3i to window 29 and use the sign given.Thus divide the product obtained from multiplying side 25 by thefunction in window 3! by the function in window 29, the result being thelength of side 24.

To find side 23, side 24 and angles F and D being given, set the disksso that the correct angles appear in windows 27 and 28. Set disk so thatthe difference between 180 degrees and the sum of angles D and F appearsin window 26. Proceed from the given side 24 following the arrows to thewindow 30 and multiply (as directed by the indicia) side 24 by thefunction in window 39. Then follow the ar rows directly to window 3| anddivide the product of side 24 and the function in window 35 by thefunction in window 3|, the result being the length of side 23.

To solve triangles having one angle greater than 90 degrees, it ismerely necessary to subtract the given angle from 179 degrees and usethe function for the resulting remainder, proceeding in calculations asabove.

Thus it is seen that the calculator presented by the invention, which issimple to use, economical to manufacture as well as being accurate incomputations, precludes the use of trigonometric tables in the solvin oftriangles.

I claim;

1. A calculator for solving triangles comprising a pair of spacedplates, one side of said plates having a geometric representationthereon of a right triangle, the other of said plates having thereon ageometric representation of an oblique triangle, a plurality of windowsin the plate with the oblique triangle, said windows being positionedadjacent each angle of the triangle, a plurality of windows in the platewith the right triangle, said windows being positioned adjacent eachside and each of the complementary angles of the right triangle, asystem of intermeshing disks rotatably mounted between the plates andadjacent the right triangle plate, a series of independent disksrotatably mounted between said plates and adjacent the oblique triangleplate, and indicia representing trigonometric functions and angles onthe disks, the said disks being movable to present the proper relatedindicia before each window to assist in the solving of the unknown angleand side values of the triangles when certain of such values are known.

2. A calculator for solving triangles comprising a pair of spacedcircular plates, one of said plates having a geometric representationinscribed thereon of a right triangle, the other of said plates havinginscribed thereon a geometric representation of an oblique triangle, aplurality of windows in the plate with the oblique triangle, saidwindows being positioned ad acent each angle of the triangle, aplurality of windows in the plate with the right triangle, said windowsbeing positioned adjacent each side and each of the complementary anglesof the right triangle, a driving disk and three driven follower disksrotatably mounted between the plates and adjacent the right triangleplate, the driving disk having its periphery extending beyond theperipheries of the plates, a series of independent disks rotatablymounted between said plates and adjacent the oblique triangle plate, theperipheries of the disks extending beyond the peripheries of the plates,and trigonometric function indicia on said rotatable disks for selectivepresentation to the plate windows to assist in the solving of theunknown angle and side values of the triangle when certain of suchvalues are known.

3. A calculator for solving triangles comprising a plate, a geometricrepresentation of a right triangle inscribed on said plate, windows inthe plate associated with the complementary angles of the inscribedtriangle and with the three sides of said triangle, rotatable disk meansto present a given angle in one of the complementary angle windows andfollower disks driven by said disk means to automatically present thecomplementary angle of the given angle in the other angle window and thetrigonometric functions of such given and complementary angles in thewindows associated with the sides of the inscribed triangle.

4. A calculator for solving triangles comprising a plate, a geometricrepresentation of a right triangle inscribed on said plate, windows inthe plate associated with the complementary angles of the inscribedtriangle and with the three sides of said triangle, rotatable disk meansto present a given angle in one of the complementary angle windows andfollower disks driven by said disk means to automatically present thecomplementary angle of the given angle in the other angle window and thetrigonometric functions of such given and complementary angles in thewindows associated with the sides of the inscribed triangle andmultiplication, division and direction indicia associated with saidwindows presenting the functions to visually instruct the user in usingthe functions to determine the unknown sides of a triangle.

WILLARD H. JENSEN.

REFERENCES CITED The following references are of record in the file ofthis patent:

' UNITED STATES PATENTS

